Homotonic algebras
Volume 195 / 2009
Studia Mathematica 195 (2009), 287-295
MSC: Primary 15A60, 16B99, 17A05, 17A15.
DOI: 10.4064/sm195-3-7
Abstract
An algebra $\mathcal{A}$ of real- or complex-valued functions defined on a set ${\bf T}$ shall be called homotonic if $\mathcal{A}$ is closed under taking absolute values, and for all $f$ and $g$ in $\mathcal{A}$, the product $f\times g$ satisfies $|f\times g|\le|f|\times|g|$. Our main purpose in this paper is two-fold: to show that the above definition is equivalent to an earlier definition of homotonicity, and to provide a simple inequality which characterizes submultiplicativity and strong stability for weighted sup norms on homotonic algebras.
